A224873 Triangle of coefficients T(n, k) (n > 0, k < n) in expansion of sin(u*x) * sin(v*x) / (cos(u*x) + cos(v*x)), read by rows.
1, 1, 1, 3, 25, 3, 17, 329, 329, 17, 155, 5325, 14301, 5325, 155, 2073, 110605, 563013, 563013, 110605, 2073, 38227, 2918825, 23904881, 45956625, 23904881, 2918825, 38227, 929569, 96075665, 1150348017, 3600524785, 3600524785, 1150348017, 96075665, 929569
Offset: 1
Examples
1; 1, 1; 3, 25, 3; 17, 329, 329, 17; ...
Links
- Michael Hardy, A "known" tangent half-angle formula?.
Programs
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PARI
{T(n, k) = local(u = 'u, v = 'v, A); if( n<0 || k>=n, 0, n = 2*n; k = 2*k + 1; A = x * O(x^n); n! * polcoeff( polcoeff( polcoeff( sin( u*x + A) * sin( v*x + A) / (cos( u*x + A) + cos( v*x + A)), n, x), k, u), n - k, v))}